Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
744 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C23×C32 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C22×C32 ◁ C2×C32×Q8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×H(3,𝔽4) | C2 | semidirect |
| 2. C32×#454 | C2 | semidirect |
| 3. C32×#355 | C2 | semidirect |
| 4. C3×#2202 | C3 | direct (N × H) |
| 5. C32×2−1+4 | C22 | semidirect |
| 11. C32×#101 | C22 | semidirect |
| 12. C3×H(3,𝔽4) | C2×C3 | semidirect |
| 13. C3×#454 | C2×C3 | semidirect |
| 14. C3×#355 | C2×C3 | semidirect |
| 29. #2202 | C32 | direct (N × H) |
| 30. C3×2−1+4 | C22×C3 | semidirect |
| 36. C3×#101 | C22×C3 | semidirect |
| 51. H(3,𝔽4) | C2×C32 | semidirect |
| 52. #454 | C2×C32 | semidirect |
| 53. #355 | C2×C32 | semidirect |
| 76. 2−1+4 | C22×C32 | semidirect |
| 82. #101 | C22×C32 | semidirect |
| 123. C32 | #2202 | direct (N × H) |
| 150. C3 | C3×#2202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×H(3,𝔽4) | 2 |
| C32×#454 | 2 |
| C32×#355 | 2 |
| C3×#2202 | 3 |